1. Technical Field
The present invention relates to a position calculating method and a position calculating device.
2. Related Art
A GPS (global positioning system) is widely known as a positioning system using a positioning signal, and is used for a position calculating device built in a mobile phone, a car navigation device, or the like. The GPS performs a position calculation operation for calculating a timepiece error and the position coordinates of a position calculating device on the basis of information, such as the positions of a plurality of GPS satellites or a pseudorange from each GPS satellite to the position calculating device.
In position calculation using a positioning signal, there is a problem in that the accuracy of position calculation is reduced due to various error factors. Accordingly, various techniques for improving the accuracy of position calculation have been proposed. For example, JP-A-8-68651 discloses a technique of correcting the position calculated using a GPS by performing an inertial navigation operation using a velocity vector of a moving body.
In the inertial navigation operation used in the past, a method of calculating a velocity vector by integrating a detected acceleration vector and then calculating a current position by adding the amount of movement corresponding to the current velocity vector to the previous position is used if an acceleration sensor is used, for example. Here, the “vector” is a term of convenience for expressing a direction and a size. In order to express the direction and the size, it is needless to say that the value of each axis in a Cartesian coordinate system or a spherical coordinate system can be used, for example. However, even if any notation is selected, it is obvious that it is equivalent to a “vector”. Therefore, in this specification, a “vector” is used as a term for expressing both the direction and the size.
However, this does not necessarily mean that a velocity vector is calculated once by performing integration of an acceleration vector whenever the acceleration vector is detected and the position is calculated (more accurately, the computed position is updated) for every calculation of the velocity vector. In a series of processing in which a velocity vector is acquired from an acceleration vector and the position is calculated from the acquired velocity vector, processing called cumulative addition for summation of a plurality of vectors is included in addition to integration. That is, one velocity vector (Expression (2) given below) is calculated by cumulative addition of a vector (Expression (1) given below) obtained by integrating a plurality of acceleration vectors detected continuously, or the current position is calculated from the previous position (computed position is updated) by cumulative addition of a plurality of calculated velocity vectors.∫t-1t{right arrow over (a)}·dt=d{right arrow over (v)}  (1){right arrow over (v)}t={right arrow over (v)}t-1+d{right arrow over (v)}  (2)
For example, the case of calculating one velocity vector from a plurality of acceleration vectors will be described. An acceleration vector is assumed to be fixed during a time until the next detection after an acceleration vector is detected (for a detection interval), even though it is a tiny amount of time in practice. Each of the plurality of acceleration vectors detected continuously is integrated at detection intervals, and cumulative addition (summation) of each integrated value is performed over a predetermined unit period. As a result, a velocity vector of a unit period is calculated. For example, in a navigation system, one-time position calculation (position update) is performed for 1 second but acceleration detection is performed many times for 1 second.
Thus, there is the following problem in a series of processing for calculating the position from the detection of an acceleration vector, which has been performed in the related art. That is, since a velocity vector is sequentially calculated while performing integration and cumulative addition of acceleration vectors detected at short detection intervals, there is a problem in that an error included in a velocity vector cumulatively increases with time. Undoubtedly, an increase in an error included in the velocity vector causes a reduction in the accuracy of position calculation.